The inversion of snow parameters from passive microwave remote sensing measurements is performed with a neural network trained with a dense media multiple scattering model. The basic idea is to use the input-output pairs generated by the scattering model to train the neural network. Once the neural network is trained, it can invert snow parameters speedily from the measurements. In this paper, we have performed simultaneous inversion of three parameters: mean-grain size of ice particles in snow, snow density, and snow temperature from five brightness temperatures. The five brightness temperatures are that of 19 GHz vertical polarization, 19 GHz horizontal polarization, 22 GHz vertical polarization, 37 GHz vertical polarization, and 37 GHz horizontal polarization. It is shown that the neural network gives good results for the inversion of parameters from the simulated data computed from the dense media radiative transfer equation which includes the effects of multiple scattering. For the simulated testing data, the absolute percentage errors for mean-grain size of ice particles and snow density are less than 10%, and the absolute error for snow temperature less than is 3-degrees-K. We also use the neural network with the trained weighting coefficients of the three-parameter model to invert the SSMI data over the Antarctica region. The algorithm inverts 30 000 sets of 5-channel brightness temperatures of Antarctica in only 10 cpu min on a VAX 3500 workstation. Validity of the inversion results is discussed in view of the limited number of parameters that we used and the much more complicated real-life situation in the Antarctica.